No one is stating that run checks don't exist. We are stating that your example is not correct.
This is the play and formation (below) where you wanted Allen to check to the right:
The QB is going to walk up to the LOS and divide the defensive box into halves. I have made them into orange and yellow boxes for convenience. He sees 4 defenders on the right and 4 on the left. This is an even box.
The WR goes in motion for the sole purpose of drawing either the left CB or left LB to follow him, making it only 3 defenders on that side of the field:
The left CB, as planned, does start to follow the motion WR but quickly recovers and goes back toward the ballcarrier when he see's its a run. Keon, being oblivious to this fact, does not block this CB. He also doesn't chip the DE like he is supposed to, barely getting a single hand on him:
Keon, having done absolutely NOTHING to help, moves on to the second level to block literal AIR, and Edwards, who was slow off the ball, puts both of his hands into Dion's back instead of engaging the DE. McGovern is meanwhile being stiff armed to the face and overpowered.
Everyone in red (below) completely misses their blocks, dooming the play. Not because of the direction, but because they suck at football.
Summary: NO, this play should NOT have gone to the other side. It was called properly and Allen diagnosed the defense properly. It would have been a huge gain if the O-line and Keon simply made their blocks.
No, NOT everyone is a viable target. Progressions and pressure, for one. But also, Joe Brady has talked in depth about how his offense has receivers whose only job is to clear out or draw attention away from where the play is meant to go, and just because they are open is not meant as an indication for Josh to go there... that they set up plays for later, etc.